DOUBLE EXPONENTIAL INTEGRABILITY OF CONVOLUTION-OPERATORS IN GENERALIZED LORENTZ-ZYGMUND SPACES

Authors
EDMUNDS DE GURKA P OPIC B
Citation
De. Edmunds et al., DOUBLE EXPONENTIAL INTEGRABILITY OF CONVOLUTION-OPERATORS IN GENERALIZED LORENTZ-ZYGMUND SPACES, Indiana University mathematics journal, 44(1), 1995, pp. 19-43
Citations number
11
Categorie Soggetti
Mathematics, General",Mathematics
Journal title
Indiana University mathematics journal → ACNP
ISSN journal
00222518
Volume
44
Issue
1
Year of publication
1995
Pages
19 - 43
Database
ISI
SICI code
0022-2518(1995)44:1<19:DEIOCI>2.0.ZU;2-N
Abstract
This paper provides estimates for an appropriate norm of the convoluti on of a function in a Lorentz space with one in a generalized Lorentz- Zygmund space. As a corollary, it is shown that the Riesz potential of a function in an appropriate generalized Lorentz-Zygmund space satisf ies a 'double exponential' integrability condition. The results extend those of Brezis-Wainger on the convolution of functions in Lorentz sp aces which lead to exponential integrability.